Plucker Relations on Schur Functions

Details Plucker Relations on Schur Functions Plucker Relations on Schur Functions

1999-07-27

arxiv.org/abs/math/9907177v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular partitions. We prove the relations as an application of a technique for turning Plucker relations into statements about Schur functions and other objects with similar definitions as determinants. We also give a quantum analog of the relations which incorporates spectral parameters. Our proofs are mostly algebraic, but the relations have a clear combinatorial side, which we discuss.

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